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<title>3.1. 数据与内存 - Hello 算法</title>
<title>3.1.   数据与内存 - Hello 算法</title>
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<div class="md-header__topic" data-md-component="header-topic">
<span class="md-ellipsis">
3.1. 数据与内存
3.1. &nbsp; 数据与内存
</span>
</div>
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<label class="md-nav__link" for="__nav_1" id="__nav_1_label" tabindex="0">
0. 写在前面
0. &nbsp; &nbsp; 写在前面
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_1">
<span class="md-nav__icon md-icon"></span>
0. 写在前面
0. &nbsp; &nbsp; 写在前面
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
<a href="../../chapter_preface/about_the_book/" class="md-nav__link">
0.1. 关于本书
0.1. &nbsp; 关于本书
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_preface/suggestions/" class="md-nav__link">
0.2. 如何使用本书
0.2. &nbsp; 如何使用本书
</a>
</li>
@ -314,7 +314,7 @@
<li class="md-nav__item">
<a href="../../chapter_preface/installation/" class="md-nav__link">
0.3. 编程环境安装
0.3. &nbsp; 编程环境安装
</a>
</li>
@ -328,7 +328,7 @@
<li class="md-nav__item">
<a href="../../chapter_preface/contribution/" class="md-nav__link">
0.4. 一起参与创作
0.4. &nbsp; 一起参与创作
</a>
</li>
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<label class="md-nav__link" for="__nav_2" id="__nav_2_label" tabindex="0">
1. 引言
1. &nbsp; &nbsp; 引言
<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
1. 引言
1. &nbsp; &nbsp; 引言
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
<a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
1.1. 算法无处不在
1.1. &nbsp; 算法无处不在
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
1.2. 算法是什么
1.2. &nbsp; 算法是什么
</a>
</li>
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<label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
2. 计算复杂度
2. &nbsp; &nbsp; 计算复杂度
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
2. 计算复杂度
2. &nbsp; &nbsp; 计算复杂度
</label>
<ul class="md-nav__list" data-md-scrollfix>
@ -462,7 +462,7 @@
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
2.1. 算法效率评估
2.1. &nbsp; 算法效率评估
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
2.2. 时间复杂度
2.2. &nbsp; 时间复杂度
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
2.3. 空间复杂度
2.3. &nbsp; 空间复杂度
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_computational_complexity/space_time_tradeoff/" class="md-nav__link">
2.4. 权衡时间与空间
2.4. &nbsp; 权衡时间与空间
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
2.5. 小结
2.5. &nbsp; 小结
</a>
</li>
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<label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
3. 数据结构简介
3. &nbsp; &nbsp; 数据结构简介
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_4">
<span class="md-nav__icon md-icon"></span>
3. 数据结构简介
3. &nbsp; &nbsp; 数据结构简介
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<label class="md-nav__link md-nav__link--active" for="__toc">
3.1. 数据与内存
3.1. &nbsp; 数据与内存
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
3.1. 数据与内存
3.1. &nbsp; 数据与内存
</a>
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<li class="md-nav__item">
<a href="#311" class="md-nav__link">
3.1.1. 基本数据类型
3.1.1. &nbsp; 基本数据类型
</a>
<nav class="md-nav" aria-label="3.1.1. 基本数据类型">
<nav class="md-nav" aria-label="3.1.1. &nbsp; 基本数据类型">
<ul class="md-nav__list">
<li class="md-nav__item">
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<li class="md-nav__item">
<a href="#312" class="md-nav__link">
3.1.2. 计算机内存
3.1.2. &nbsp; 计算机内存
</a>
</li>
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<li class="md-nav__item">
<a href="../classification_of_data_structure/" class="md-nav__link">
3.2. 数据结构分类
3.2. &nbsp; 数据结构分类
</a>
</li>
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<li class="md-nav__item">
<a href="../summary/" class="md-nav__link">
3.3. 小结
3.3. &nbsp; 小结
</a>
</li>
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<label class="md-nav__link" for="__nav_5" id="__nav_5_label" tabindex="0">
4. 数组与链表
4. &nbsp; &nbsp; 数组与链表
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_5">
<span class="md-nav__icon md-icon"></span>
4. 数组与链表
4. &nbsp; &nbsp; 数组与链表
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
4.1. 数组Array
4.1. &nbsp; 数组Array
</a>
</li>
@ -757,7 +757,7 @@
<li class="md-nav__item">
<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
4.2. 链表LinkedList
4.2. &nbsp; 链表LinkedList
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
4.3. 列表List
4.3. &nbsp; 列表List
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
4.4. 小结
4.4. &nbsp; 小结
</a>
</li>
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<label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
5. 栈与队列
5. &nbsp; &nbsp; 栈与队列
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_6">
<span class="md-nav__icon md-icon"></span>
5. 栈与队列
5. &nbsp; &nbsp; 栈与队列
</label>
<ul class="md-nav__list" data-md-scrollfix>
@ -846,7 +846,7 @@
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
5.1. 栈Stack
5.1. &nbsp;Stack
</a>
</li>
@ -860,7 +860,7 @@
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
5.2. 队列Queue
5.2. &nbsp; 队列Queue
</a>
</li>
@ -874,7 +874,7 @@
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
5.3. 双向队列Deque
5.3. &nbsp; 双向队列Deque
</a>
</li>
@ -888,7 +888,7 @@
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
5.4. 小结
5.4. &nbsp; 小结
</a>
</li>
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<label class="md-nav__link" for="__nav_7" id="__nav_7_label" tabindex="0">
6. 散列表
6. &nbsp; &nbsp; 散列表
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_7">
<span class="md-nav__icon md-icon"></span>
6. 散列表
6. &nbsp; &nbsp; 散列表
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
6.1. 哈希表HashMap
6.1. &nbsp; 哈希表HashMap
</a>
</li>
@ -961,7 +961,7 @@
<li class="md-nav__item">
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
6.2. 哈希冲突处理
6.2. &nbsp; 哈希冲突处理
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_hashing/summary/" class="md-nav__link">
6.3. 小结
6.3. &nbsp; 小结
</a>
</li>
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<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
7. 二叉树
7. &nbsp; &nbsp; 二叉树
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_8">
<span class="md-nav__icon md-icon"></span>
7. 二叉树
7. &nbsp; &nbsp; 二叉树
</label>
<ul class="md-nav__list" data-md-scrollfix>
@ -1038,7 +1038,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
7.1. 二叉树Binary Tree
7.1. &nbsp; 二叉树Binary Tree
</a>
</li>
@ -1052,7 +1052,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
7.2. 二叉树遍历
7.2. &nbsp; 二叉树遍历
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
7.3. 二叉搜索树
7.3. &nbsp; 二叉搜索树
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
7.4. AVL 树 *
7.4. &nbsp; AVL 树 *
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_tree/summary/" class="md-nav__link">
7.5. 小结
7.5. &nbsp; 小结
</a>
</li>
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<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
8. 堆
8. &nbsp; &nbsp;
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_9">
<span class="md-nav__icon md-icon"></span>
8. 堆
8. &nbsp; &nbsp;
</label>
<ul class="md-nav__list" data-md-scrollfix>
@ -1149,7 +1149,7 @@
<li class="md-nav__item">
<a href="../../chapter_heap/heap/" class="md-nav__link">
8.1. 堆Heap
8.1. &nbsp;Heap
</a>
</li>
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<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
9. 图
9. &nbsp; &nbsp;
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_10">
<span class="md-nav__icon md-icon"></span>
9. 图
9. &nbsp; &nbsp;
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
<a href="../../chapter_graph/graph/" class="md-nav__link">
9.1. 图Graph
9.1. &nbsp;Graph
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
9.2. 图基础操作
9.2. &nbsp; 图基础操作
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
9.3. 图的遍历
9.3. &nbsp; 图的遍历
</a>
</li>
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<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
10. 查找算法
10. &nbsp; &nbsp; 查找算法
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_11">
<span class="md-nav__icon md-icon"></span>
10. 查找算法
10. &nbsp; &nbsp; 查找算法
</label>
<ul class="md-nav__list" data-md-scrollfix>
@ -1297,7 +1297,7 @@
<li class="md-nav__item">
<a href="../../chapter_searching/linear_search/" class="md-nav__link">
10.1. 线性查找
10.1. &nbsp; 线性查找
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
10.2. 二分查找
10.2. &nbsp; 二分查找
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_searching/hashing_search/" class="md-nav__link">
10.3. 哈希查找
10.3. &nbsp; 哈希查找
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_searching/summary/" class="md-nav__link">
10.4. 小结
10.4. &nbsp; 小结
</a>
</li>
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<label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="0">
11. 排序算法
11. &nbsp; &nbsp; 排序算法
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_12">
<span class="md-nav__icon md-icon"></span>
11. 排序算法
11. &nbsp; &nbsp; 排序算法
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
<a href="../../chapter_sorting/intro_to_sort/" class="md-nav__link">
11.1. 排序简介
11.1. &nbsp; 排序简介
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
11.2. 冒泡排序
11.2. &nbsp; 冒泡排序
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
11.3. 插入排序
11.3. &nbsp; 插入排序
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
11.4. 快速排序
11.4. &nbsp; 快速排序
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
11.5. 归并排序
11.5. &nbsp; 归并排序
</a>
</li>
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<li class="md-nav__item">
<a href="../../chapter_sorting/summary/" class="md-nav__link">
11.6. 小结
11.6. &nbsp; 小结
</a>
</li>
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<li class="md-nav__item">
<a href="#311" class="md-nav__link">
3.1.1. 基本数据类型
3.1.1. &nbsp; 基本数据类型
</a>
<nav class="md-nav" aria-label="3.1.1. 基本数据类型">
<nav class="md-nav" aria-label="3.1.1. &nbsp; 基本数据类型">
<ul class="md-nav__list">
<li class="md-nav__item">
@ -1596,7 +1596,7 @@
<li class="md-nav__item">
<a href="#312" class="md-nav__link">
3.1.2. 计算机内存
3.1.2. &nbsp; 计算机内存
</a>
</li>
@ -1625,8 +1625,8 @@
<h1 id="31">3.1. 数据与内存<a class="headerlink" href="#31" title="Permanent link">&para;</a></h1>
<h2 id="311">3.1.1. 基本数据类型<a class="headerlink" href="#311" title="Permanent link">&para;</a></h2>
<h1 id="31">3.1. &nbsp; 数据与内存<a class="headerlink" href="#31" title="Permanent link">&para;</a></h1>
<h2 id="311">3.1.1. &nbsp; 基本数据类型<a class="headerlink" href="#311" title="Permanent link">&para;</a></h2>
<p>谈到计算机中的数据我们能够想到文本、图片、视频、语音、3D 模型等等,这些数据虽然组织形式不同,但都是由各种基本数据类型构成的。</p>
<p><strong>「基本数据类型」是 CPU 可以直接进行运算的类型,在算法中直接被使用</strong></p>
<ul>
@ -1866,7 +1866,7 @@
</div>
</div>
</div>
<h2 id="312">3.1.2. 计算机内存<a class="headerlink" href="#312" title="Permanent link">&para;</a></h2>
<h2 id="312">3.1.2. &nbsp; 计算机内存<a class="headerlink" href="#312" title="Permanent link">&para;</a></h2>
<p>在计算机中,内存和硬盘是两种主要的存储硬件设备。「硬盘」主要用于长期存储数据,容量较大(通常可达到 TB 级别)、速度较慢。「内存」用于运行程序时暂存数据,速度较快,但容量较小(通常为 GB 级别)。</p>
<p><strong>算法运行中,相关数据都被存储在内存中</strong>。下图展示了一个计算机内存条,其中每个黑色方块都包含一块内存空间。我们可以将内存想象成一个巨大的 Excel 表格,其中每个单元格都可以存储 1 byte 的数据,在算法运行时,所有数据都被存储在这些单元格中。</p>
<p><strong>系统通过「内存地址 Memory Location」来访问目标内存位置的数据</strong>。计算机根据特定规则给表格中每个单元格编号,保证每块内存空间都有独立的内存地址。自此,程序便通过这些地址,访问内存中的数据。</p>
@ -1951,7 +1951,7 @@
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